In [31]:
%runfile H3.py
In [32]:
from utils import (make_M_alphas,
make_poly_from_edges,
poly_equiv, tri0, tri1, tri2, cycle_poly, std_poly,
poly_gl2_orbit_reps,
aas_triangle_gl2_orbit_reps,
square_parameters,
aaa_triangle_parameters,
aas_triangle_parameters,
hexagon_parameters)
from polyhedra import all_poly_types, poly_type, poly_types
In [33]:
d = 21
In [34]:
kdata = make_k(d)
k = kdata['k']
w = kdata['w']
zero = k(0)
one = k(1)
Ireps = kdata['Ireps']
inf = cusp(infinity, k)
k.class_number()
Out[34]:
In [35]:
alphas, sigmas = alpha_sigma_data(d, verbose=False)
#alphas = precomputed_alphas(k)
M_alphas, alpha_inv = make_M_alphas(alphas)
print("{} alphas".format(len(alphas)))
#sigmas = [cusp(s,k) for s in [oo, (w)/(2), (w + 1)/(3), (-w - 1)/(3), (-w + 1)/(3), (w - 1)/(3)]]
print("{} sigmas".format(len(sigmas)))
In [36]:
FD_proj = plot_FunDomain_projection(k, alphas, sigmas)
FD_proj.show(figsize=[10,10])
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sigmas
Out[37]:
In [38]:
alphas
Out[38]:
In [39]:
polys, hemis = all_polyhedra(k, alphas)
print("{} polyhedra constructed".format(len(polys)))
In [40]:
poly_types(polys)
Out[40]:
In [41]:
all_poly_types(polys)
Out[41]:
In [42]:
assert len(polys)==23
for G in polys: show(G)
In [43]:
triangles = [make_poly_from_edges(t,k) for t in sum([[F for F in G.faces() if len(F)==3] for G in polys],[])]
squares = [make_poly_from_edges(t,k) for t in sum([[F for F in G.faces() if len(F)==4] for G in polys],[])]
hexagons = [make_poly_from_edges(t,k) for t in sum([[F for F in G.faces() if len(F)==6] for G in polys],[])]
aaa_triangles = [T for T in triangles if is_poly_principal(T)]
aas_triangles = [T for T in triangles if not is_poly_principal(T)]
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[len(t) for t in [aaa_triangles, aas_triangles, squares, hexagons]]
Out[44]:
In [45]:
aaa_triangles0 = poly_gl2_orbit_reps(aaa_triangles, alphas)
aas_triangles0 = aas_triangle_gl2_orbit_reps(aas_triangles, alphas)
squares0 = poly_gl2_orbit_reps(squares, alphas)
hexagons0 = poly_gl2_orbit_reps(hexagons, alphas)
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[len(t) for t in [aaa_triangles0, aas_triangles0, squares0, hexagons0]]
Out[46]:
In [53]:
triangles0 = [T for T in aaa_triangles0 if any(poly_equiv(T, t) for t in [tri0(k), tri1(k), tri2(k)])]
triangles1 = [T for T in aaa_triangles0 if not any(poly_equiv(T, t) for t in [tri0(k), tri1(k), tri2(k)])]
triangles0, triangles1
Out[53]:
In [48]:
aaa = [aaa_triangle_parameters(T, alphas, M_alphas) for T in triangles1]
In [49]:
aas = [aas_triangle_parameters(T, alphas, M_alphas, sigmas) for T in aas_triangles0]
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squ = [square_parameters(S, alphas, M_alphas, alpha_inv) for S in squares0]
In [51]:
hex = [hexagon_parameters(H, alphas, M_alphas) for H in hexagons0]
In [52]:
plot_Bianchi_diagram(k,hemis)
Out[52]:
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